Parabolic Curve

Vertical Parabolic Curve
Vertical curves are used to provide gradual change between two adjacent vertical grade lines. The curve used to connect the two adjacent grades is parabola. Parabola offers smooth transition because its second derivative is constant. For a downward parabola with vertex at the origin, the standard equation is
 

$x^2 = -4ay$   or   $y = -\dfrac{x^2}{4a}$.

 

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